Projection refers to the reduction of a fractional factorial design
to a full factorial design by dropping out some of the factors of the
design. Any fractional factorial design of resolution, can be reduced to complete factorial
designs in any subset of factors. For example, consider the
2 design. The resolution of this design
is four. Therefore, this design can be reduced to full factorial designs
in any three () of the original seven factors (by
dropping the remaining four of factors). Further, a fractional factorial
design can also be reduced to a full factorial design in any of the original factors, as long as
these factors are not part of the generator
in the defining relation. Again consider the 2 design. This design can be reduced
to a full factorial design in four factors provided these four factors
do not appear together as a generator in the defining relation. The complete
defining relation for this design is:Therefore, there are seven four factor
combinations out of the 35 () possible four-factor combinations
that are used as generators in the defining relation. The designs with
the remaining 28 four factor combinations would be full factorial 16-run
designs. For example, factors , , and do not occur as a generator in the
defining relation of the 2 design. If the remaining factors,
, and , are dropped, the 2 design will reduce to a full factorial
design in , , and .
can be reduced to complete factorial
designs in any subset of 
factors. For example, consider the
2
design. The resolution of this design
is four. Therefore, this design can be reduced to full factorial designs
in any three (
) of the original seven factors (by
dropping the remaining four of factors). Further, a fractional factorial
design can also be reduced to a full factorial design in any 
of the original factors, as long as
these 
factors are not part of the generator
in the defining relation. Again consider the 2
design. This design can be reduced
to a full factorial design in four factors provided these four factors
do not appear together as a generator in the defining relation. The complete
defining relation for this design is:
Therefore, there are seven four factor
combinations out of the 35 (
) possible four-factor combinations
that are used as generators in the defining relation. The designs with
the remaining 28 four factor combinations would be full factorial 16-run
designs. For example, factors 
, 
, 
and 
do not occur as a generator in the
defining relation of the 2
design. If the remaining factors,
, 
and 
, are dropped, the 2
design will reduce to a full factorial
design in 
, 
, 
and 
.